Gaza City, Gaza - Palestinians seeking refuge at Gaza's largest hospital and staff said they were trapped in increasingly horrific conditions Saturday, with two premature infants dying due to lack of electricity as Israel is accused of besieging the facility.

The Israeli military has denied that it is attacking at Al-Shifa hospital, but has also repeatedly accused Hamas of using medical facilities as command centers and hideouts – a charge the Palestinian militant group, as well as medical organizations, deny.

The gun battles and intense bombardment around the compound came as Israel pressed deep into Gaza City, five weeks on from the Hamas attack that killed 1,200 people and led to the kidnapping of some 240 more.

"Shooting is never stopping, airstrikes are unabated as well as artillery shells," said a witness who spoke on condition of anonymity. "There are dozens of bodies around the complex that nobody can reach."

Though tens of thousands of people have been forced to flee south, many have taken shelter in northern Gaza's hospitals which have been repeatedly hit by explosive strikes and gunfire, with the Palestinian Red Crescent Society directly accusing Israeli snipers of shooting people attempting to flee.

"The hospital is besieged, with no option to bring in the corpses and injured people sprawled outside. There is no movement in or out of the hospital," said Physicians for Human Rights Israel, citing doctors at Al-Shifa.

The Israeli doctors' group added that due to the lack of electricity, the neonatal intensive care unit has stopped working and two premature infants have died – leaving the lives of 37 other infants at risk.

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"The situation in Al-Shifa is truly catastrophic," said Ann Taylor, head of the Palestinian Territories mission for the medical charity Doctors Without Borders (MSF).

The suffering in Gaza has prompted growing calls for a halt in five weeks of fighting in order to protect civilian lives and allow humanitarian aid into the densely populated territory.

French President Emmanuel Macron said Israel had the right to defend itself but urged it to stop strikes on civilians in Gaza: "These babies, these ladies, these old people are bombed and killed."

Concern has also come from the US, with Secretary of State Antony Blinken saying Friday: "Far too many Palestinians have been killed."

Israeli Prime Minister Benjamin Netanyahu pushed back, saying the responsibility for any harm to civilians lies with Hamas.

"Israel does everything in its power to avoid harming civilians and urges them to leave the battle areas," he said.

Palestinian health authorities have put the death toll in Gaza at over 11,000, the majority of whom are women and children.